Phase unwrapping is an important problem in the areas of Optical Metrology, Synthetic Aperture Radar (SAR) image analysis and Magnetic Resonance Imaging (MRI) analysis. These images are becoming larger in size and, particularly, the availability and need for processing of SAR and MRI data has increased significantly with the acquisition of remote sensing data and the popularization of magnetic resonators in clinical diagnosis. Therefore, it is important to develop faster and accurate phase unwrapping algorithms. In this paper, we propose a parallel multigrid algorithm of a phase unwrapping method named accumulation of residual maps (ARM), which builds on a serial algorithm that consists of the minimization of a cost function; minimization achieved by means of a serial Gauss-Seidel kind algorithm. Our algorithm also optimizes the original cost function, but unlike the original work, our algorithm is a parallel Jacobi class with alternated minimizations. This strategy is known as the chessboard type where red pixels can be updated in parallel at same iteration since they are independent. Similarly, black pixels can be updated in parallel in an alternating iteration. We present parallel implementations of our algorithm for different parallel multicore architecture such as CPU-multicore, Xeon Phi coprocessor and Nvidia GPU. In all the cases, we obtain a superior performance of our parallel algorithm when compared to the original serial version. In addition, we present a detailed comparative of the performance of the developed parallel versions.